Final answer:
To solve the inequality, we simplify and combine like terms, find a common denominator, and divide by the coefficient of x. When we divide by a negative, we reverse the inequality sign, resulting in x being greater than roughly 2.29. Hence, the correct option is x > 2.
Step-by-step explanation:
To solve the inequality -x < -2 - (4x + 6) - 5/2x, let's first simplify the inequality by distributing the negative sign and combining like terms.
Step 1: Distribute the negative sign through the parenthesis.
-x < -2 - 4x - 6 - 5/2x
Step 2: Combine like terms (-x and -5/2x are like terms).
-x - 5/2x < -2 - 6
Step 3: Combine the x terms by finding a common denominator, which is 2.
-2/2x - 5/2x < -8
Step 4: Add the x terms together.
-7/2x < -8
Step 5: Divide both sides of the inequality by -7/2 (and remember to reverse the inequality sign when dividing by a negative number).
x > 8 / (7/2)
Step 6: Simplify the fraction by multiplying both numerator and denominator by 2.
x > 16/7
Since 16/7 is approximately 2.29, which is greater than 2, the correct option is that x > 2.